Sinusoidal Functions

Quote:

Originally Posted by Random-Hero-

Hey all, right now I'm covering Sinusoidal Functions of form

f(x)= a sin[k(x-d)]+c and f(x)= a cos[k(x-d)]+c

And I was just wondering if you guys could clarify my answer for me and tell me if I'm correct, or I've made an error.

Question:
Consider the function y = 4sin [2 ( x+(2pi/3)] - 5

a) What is the amplitude?
b) What is the period?
c) Describe the phase shift.
d) Describe the vertical translation
e) graph the function. Compare the graph to the properties in parts a) to d)
f) Describe the x-intercepts of the function. Explain your answer

Answers thus far:

a) 4
b) pi
c) 2pi/3 to the left
d) 5 units down

e) I have no idea how to graph this :|

f) Also, stumped.

Your thoughts and input are greatly appreciated! thanks!

Hello;

Your answers to parts a, b & d are correct but as for answer c) it is 4$\displaystyle \pi$/3 to the left, as 4sin(2x + 4$\displaystyle \pi$/3) -5

To make the graph of this function:
1. First make a dotted at the mean position i.e y= -5
2. Mark with dotted line the amplitude i.e on y= -1 and -9
3. Now mark the point -2$\displaystyle \pi$/3,-5 (you can check sin [2 ( x+(2$\displaystyle \pi$/3)] to be zero at this -2$\displaystyle \pi$/3)
4. Now starting from the point(-2$\displaystyle \pi$/3,-5) ,taking y=-5 as the mean position line and considering the limits i.e amplitude in step 2, draw the graph quite similar to sin(0.5x). Add $\displaystyle \pi$ to -2$\displaystyle \pi$/3 to get the point on x-coordinate where one complete cycle ends.

For part f) there will be no x-intercepts because max. value of this function is -1.